70 RESULTANTS OF FORCES. 



By a similar resolution of all the forces we shall have them 

 replaced by the forces 



Si; si; y.. 



ing at along the axes, and the couples 



2: (/if Yz)**L suppose, in the plane of (y, z) t 



Let R be the resultant of the forces which act at ; a, I, c 



the angles its direction makes with the axes ; then, by A 



COS a = -jr- , COS = -jj- , COS C = 



Let G be the moment of the couple which is tli resultant 

 of the three couples L, M, N ; X, /i, v the angL 

 makes with the co-ordinate axes ; then, by Art. 50, 



N 



convention adopted in the present Article for distin- 

 guishing the signs of couples agrees with that in Art. 41 when 

 the axes of a:, y t and z are drawn as in the present ii jin . l.ut 

 the conventions will not n- ssarily coim-idc if the figure be 

 modified; for example, if the axes of y and z be retain' i 



li^ure, but the positive part of the axis of x din-eted to the 

 left instead of the right, they will not coincide. The conven- 

 tion of the present Article is that which we shall her 

 always retain. 



To find the conditions of eqv of 'any number of 



forces acting on a rigid body in any directions. 



A system of forces acting on a rigid body can always 

 be reduced to a single force and a couple. Since these can- 



